The prior art teaches extracting information from images by deconvolution by the transformation of the desired quantity (or image) by Fourier transform and subsequent arithmetic operations. Fourier transform enables the change of an image from the spatial domain to the frequency domain, while the inverse Fourier transform enables transformation from the frequency domain to the spatial domain. In the frequency domain, the computation of deconvolution with another function also in the same frequency domain requires a simple arithmetic operation, whereas in the spatial domain the deconvolution operation requires multiple steps. The added required steps in the spatial domain render deconvolution highly inefficient compared to deconvolution in the frequency domain, i.e. the same operation can be performed in the frequency domain more efficiently. This is why a tool that allows minimal operations to compute deconvolution is beneficial whenever a large number of images having multiple pixels need to be processed to extract information contained therein.
Furthermore some images, particularly those obtained from medical images, contain high amounts of noise that may render some Fourier based and other deconvolution methods ineffective. The present application describes a method that is an improvement of a medical imaging method utilizing a deconvolution method that is highly tolerant of noise contained in images. The deconvolution method provides a technique of extracting quantitative information on organ function from existing data. Methods previously in use could not provide this information except by invasive methods which expose patients to an unacceptable degree of risk.
The present invention relates to noninvasive diagnostic procedures for producing functional images from static, non-functional images. The new images are useful in determining organ activity, or linear response. The invention utilizes an array processor for the process of deconvolution to obtain the new images.
Much previous work has been done using dynamic scintigraphy to determine organ function. Such work required direct, invasive, sampling of organ efflux to measure the changing concentration of an injected indicator over time. See e.g. Chinard and Enns, "Relative Renal Excretion Patterns of Sodium Ion, Chloride Ion, Urea, Water, and Glomerular Substances", Am. J. Physiol. (1955) 182:247-250.
The formulations used in prior invasive techniques have established the mathematics involved in organ function analysis by indicator-dilution methodology. See e.g. Meier and Zeirler, "On the Theory of Indicator Dilution Method for Measurement of Blood Flow and Volume", J. App. Physiol. (1954) 6:731-744.
Methodology to reliably determine the absolute perfusion rate of an organ by a noninvasive technique, previously unavailable, is clinically important in certain diseases, organ transplantation and determination of the effects of various pharmaceutical agents. Such methodology can be used to establish diagnoses and monitor disease progression as well as response to therapy. In the past, invasive techniques with microspheres or contrast media have been used experimentally to measure flow per unit volume or weight of the organ. See e.g. Eigler et al., "Digital Angiographic Impulse Response Analysis of Regional Myocardial Perfusion: Linearity, Reproducibility, Accuracy, and Comparison With Conventional Indicator Dilution Curve Parameters in Phantom and Canine Models", Circ. Res. (1989) 64:853-866.
Previous work with dynamic scintigraphic methods, which have the virtue of being noninvasive, has provided information from which only comparative spatial and temporal evaluations could be made, i.e., one region of an organ compared to another region, one kidney compared to the other. Peters et al., "Noninvasive Measurement of Renal Blood Flow using DTPA. In: Bischof-Delaloye A, and Blaufox MD, eds., Radionuclides in Nephrology, Karger, New York (1987), pp.26-30; and Alazraki et al., "Reliability of Radionuclide Angiography and Renography to Detect Varying Degrees of Impaired Renal Artery Flow". In: Bischof-Delaloye A, and Blaufox MD, eds., Radionuclides in Nephrology, Karger, New York (1987), pp. 82-86. It has been shown that the ratio of the slopes of the initial ascending portion of the renal time-activity curve is proportional to the relative renal blood flow. Ford et al., "The Radionuclide Renogram as a Predictor of Relative Renal Blood Flow", Radiology (1983) 149:819-821. These methods continue to prove clinically useful even though they face limitations such as dependence on the shape of injected activity, recirculation effects, and distribution of tracer to other compartments. Ash et al., "Quantitative Assessment of Blood Flow in Paediatric Recipients of Renal Transplants", J. Nucl. Med. (1988) 29:791-792.
More recently, attempts have been made to improve the methods described above by deconvolving the input-output time activity curves recorded by dynamic scintigraphy and thereby reduce dependence on empirical approximations. Nimmon et al., "Practical Application of Deconvolution Techniques to Dynamic Studies", In: Medical Radionuclide Imaging. Vienna:IAEA 1981; pp. 367-380; and Russell, "Estimation of Glomerular Filtration Rate Using .sup.99m Tc DTPA and the Gamma Camera", Eur. J. Nucl. Med. (1987) 12:548-552.
Several attempts have been made to determine flow directly from measured time activity curves without involving deconvolution procedures. Quantitative measurements of renal blood flow obtained by combining scintigraphy and ultrasound have been reported. Lear et al., "Quantitative Measurement of Renal Perfusion Following Transplant Surgery", J. Nucl. Med. (1988) 29:1656-1661. Real time ultrasound was used to determine the volume of the femoral artery from which the activity in a region of interest was measured. Thus, the activity of the tracer per unit volume of arterial blood, C.sub.a (t), was used as the input function and A.sub.k was the measured activity over the kidney. T was set to 5 sec. The equation utilized was ##EQU1## an approximation to the convolution integral ##EQU2##
Equation A represents a modification of the formulation proposed to describe the uptake of a tracer in an organ from measurements of the arterial and venous concentrations (input B(t) and output A(t)). Meier and Zierler, "On the Theory of Indicator Dilution Method for Measurement of Blood Flow and Volume", J. App. Physiol. (1954) 6:731-744.
Since such measurements are available only with invasive techniques it has been proposed that the output function, i.e. the concentration of tracer in the venous efflux could be set to zero during the very early interval of tracer uptake. Mullani and Gould, "First-pass Measurements of Regional Blood Flow with External Detectors", J. Nucl. Med. (1983) 24:577-581. This assumption leads to equation A. Comparing equation A with equation B, h(t-t') must be set to constant=F. In other words, tracer particles accumulate at a constant rate which implies that, under physiological conditions, tracer particles must remain within the region or organ supplied by the input. This holds true only when microspheres are used.
It has been reported that the kidney time activity curves have the same shape as the integrated arterial time activity curves. Peters et al., "Noninvasive Measurement of Renal Blood Flow (RBF) with DTPA", J. Nucl. Med. (1987) 28, #4(suppl):646. Even though under these circumstances the measured organ activity is proportional to blood flow, F, and the integral of the arterial concentration over time, it is questionable if equation A, even when integrated over the first time points, is appropriate for estimating blood flow to the organ. This is because mean transit time for most vascular beds, including the kidney are such that clinically useful tracers such as DTPA and hippuran, which are not administered as microspheres, leave the organ quickly.
Although several methods exist for performing deconvolution numerically, the methods are plagued by instabilities in the presence of noise. Szabo et al., "Effects of Statistical Noise and Digital Filtering on the Parameters Calculated From the Impulse Response Function", Eur. J. Nucl. Med. (1987) 13:148-154.